Given the following data for the number of defects per spool of cable. OBSERVATION

1 2 3 4 5 6 7 8 9 10 11 12 13 14
Number of defects 2 3 1 0 1 3 2 0 2 1 3 1 2 0
a.
Determine three-sigma control limits using the above data. (Do not round intermediate calculations. Round your final answers to 2 decimal places. Leave no cells blank - be certain to enter "0" wherever required. Round up any negative control limit value to zero.)

UCL
LCL
b. Is the process in control?
Yes
No

a.

UCL = 5.17

LCL = 0.00

b.) Yes

The process is in control

Explanation:

Number of observations = 14

Total number of defects = 2+3+1+0+1+3+2+0+2+1+3+1+2+0 = 21

X = (number of defects)/(observation)

X = 21/14

= 1.50

UCL = upper control limit

= X+z√X

= 1.5+3√1.5

= 1.5+3.674234614

= 5.17 to 2 decimal places

LCL = lower control limit

= X-z√X

= 1.5-3√1.5

= -2.17

= 0.00

B.)

From the above, we have the number of defects to be within the control limits of 0 to 5.17, therefore we can conclude that the process is in control

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